We present the application of a weighted least-squares technique to extract parameter estimates in linear models when all variables are subject to error and the goal of the investigation is the value of the parameters themselves. We assume that the relative variances of the variables are known and that the errors between variables are independent. The method of parameter estimation for linear functional relationships is presented, and we describe its differences from linear regression. We discuss how to obtain confidence intervals for the parameter estimates with an emphasis on computer Monte Carlo simulations. An explicit example related to measurements of lung volume changes is presented. An eigenvalue analysis of the data pertaining to the number of independent variables and a physical interpretation of the data space are also discussed.